In optical fibers composed of quartz glass materials, in order to obtain fibers having a high numerical aperture (NA) by increasing a difference of refractive index (.DELTA.n) between a core and a cladding and to use pure SiO.sub.2 glass having excellent radiation resistance as a core material, it is heretofore known to use quartz glass containing fluorine which decreases a refractive index of the quartz glass as a material for the cladding, as disclosed in, for example, U.S. Pat. Nos. 4,082,420 and 4,161,505. However, quartz glass containing a large amount of fluorine, though having a decreased refractive index by, for example, 0.5% than that of pure SiO.sub.2 glass, is soft as reported by K. Rau et al., Topical Meeting on Optical Fiber Transmission (1977) and likely to be scratched and also inferior in terms of chemical resistance and the like.
In order to overcome the above-described disadvantage, it has been proposed that a fiber preform composed of a glass rod 1 for a core and a glass layer 3 for a cladding as shown in FIG. 1 is inserted in a quartz tube and united into one body, thereby to form a fiber preform having a quartz-jacketed structure 5 as shown in FIG. 2. However, this improved process has many problems such that bubbling frequently occurs from the interface between the cladding and the jacket upon uniting the fiber preform with the quartz tube; the fiber diameter tends to vary or breaking of the fiber occurs upon drawn the jacketed preform; and the like. Further, when a plurality of fibers prepared from the preform as shown in FIG. 1 are bundled up to constitute an image fiber, etc., a bubbling phenomenon is frequently observed in a collapsing step for uniting the fiber into a bundle, thus making it difficult to obtain satisfactory products.